This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374793 #17 Jul 20 2024 18:43:13 %S A374793 2,1260,27935107200,29564884570506808579056000 %N A374793 a(n) is the largest k such that tau(k)^n >= k. %C A374793 Let prime(j)# denote the product of the first j primes, A002110(j); then %C A374793 a(1) = prime(1)# = 2, %C A374793 a(2) = 6*prime(4)# = 1260, %C A374793 a(3) = 2880*prime(8)# = 2.7935...*10^10, %C A374793 a(4) = 907200*prime(16)# = 2.9564...*10^25, %C A374793 a(5) >= 259459200*prime(30)# = 8.2015...*10^54, %C A374793 a(6) >= 3238237626624000*prime(52)# = 3.4403...*10^111, %C A374793 a(7) >= 248818180782850398720000*prime(91)# = 5.4351...*10^218. %e A374793 27935107200 = 2^7 * 3^3 * 5^2 * 7^1 * 11^1 * 13^1 * 17^1 * 19^1, %e A374793 so tau(27935107200) = (7+1)*(3+1)*(2+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) = 8*4*3*2*2*2*2*2 = 3072; 3072^3 = 28991029248 > 27935107200, and there is no larger number k such that tau(k)^3 >= k, so a(3) = 27935107200. %Y A374793 Cf. A000005, A035033, A056757, A056758. %K A374793 nonn,more %O A374793 1,1 %A A374793 _Jon E. Schoenfield_, Jul 20 2024